Consider a radioactive nuclear decay series A → B → C→ AA, AB, C..., and assume at time t = 0 only nuclei of type A are present. with decay constants • Write down the differential number, dNB, of nuclei of type B at time t in terms of the decay constants AA and XB. Now integrate your expression to find the number of nuclei of type B at time t, i.e. NB(t). [ Hint: multiply by et and use integration by parts. Don't forget the integration constant!] In the case of the actinide series (e.g. half-life of 238 U is 4.47 x 10⁹ years, very much greater than the daughter nuclei!) show that the decay chain is in secular equilibrium, i.e. all the daughter nuclei have essentially equal activities.
Consider a radioactive nuclear decay series A → B → C→ AA, AB, C..., and assume at time t = 0 only nuclei of type A are present. with decay constants • Write down the differential number, dNB, of nuclei of type B at time t in terms of the decay constants AA and XB. Now integrate your expression to find the number of nuclei of type B at time t, i.e. NB(t). [ Hint: multiply by et and use integration by parts. Don't forget the integration constant!] In the case of the actinide series (e.g. half-life of 238 U is 4.47 x 10⁹ years, very much greater than the daughter nuclei!) show that the decay chain is in secular equilibrium, i.e. all the daughter nuclei have essentially equal activities.
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![Consider a radioactive nuclear decay series A → B → C →
AA, AB, AC..., and assume at time t = 0 only nuclei of type A are present.
with decay constants
• Write down the differential number, dNB, of nuclei of type B at time t in terms of
the decay constants AA and AB.
Now integrate your expression to find the number of nuclei of type B at time t,
i.e. NB(t).
[ Hint: multiply by et and use integration by parts. Don't forget the integration
constant!]
• In the case of the actinide series (e.g. half-life of 238 U is 4.47 × 10⁹ years, very
much greater than the daughter nuclei!) show that the decay chain is in secular
equilibrium, i.e. all the daughter nuclei have essentially equal activities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa94ef811-7aeb-45cc-a8c4-872250660697%2F2985f69d-8c6d-4728-9197-00c709601c2d%2Fska5rwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a radioactive nuclear decay series A → B → C →
AA, AB, AC..., and assume at time t = 0 only nuclei of type A are present.
with decay constants
• Write down the differential number, dNB, of nuclei of type B at time t in terms of
the decay constants AA and AB.
Now integrate your expression to find the number of nuclei of type B at time t,
i.e. NB(t).
[ Hint: multiply by et and use integration by parts. Don't forget the integration
constant!]
• In the case of the actinide series (e.g. half-life of 238 U is 4.47 × 10⁹ years, very
much greater than the daughter nuclei!) show that the decay chain is in secular
equilibrium, i.e. all the daughter nuclei have essentially equal activities.
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Where did you get the first part of b) from? Before multiplying it by e- landaBt
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